Finite Group Databasebeta

← #27089296

Subgroups — #27089296

Order 12032.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256684C211yesmaximal, characteristic, complemented
2C2×#15689657C211yesmaximal, characteristic, complemented
3#20254789C214yesmaximal, complemented
4#20254762C212yesmaximal, complemented
5#20254751C212yesmaximal, complemented
6#20254740C214yesmaximal, complemented
7#20254726C212yesmaximal, complemented
8#20254715C212yesmaximal, complemented
9#20253211C212yesmaximal, complemented
10#20253195C211yesmaximal, characteristic, complemented
11#20253187C211yesmaximal, characteristic, complemented
12#20253018C212yesmaximal, complemented
13#20253007C212yesmaximal, complemented
14#20252883C212yesmaximal, complemented
15#20252862C211yesmaximal, characteristic, complemented
16#20252854C211yesmaximal, characteristic, complemented
17C2×C47×#423C211yesmaximal, characteristic, complemented
18C2×#13094057C2212yes—
19C2×#13094052C2212yes—
20#15689680C2211yescharacteristic
21#15689680C2211yescharacteristic, complemented
22#15689680C2211yescharacteristic, complemented
23#15689673C2211yescharacteristic
24#15689673C2211yescharacteristic, complemented
25#15689673C2211yescharacteristic, complemented
26#15689657—21no—
27#15689657—21no—
28#15689657—21no—
29#15689657—21no—
30#15689657—21no—
31#15689657—21no—
32#15689657—21no—
33#15689657—21no—
34#15689657C2212yes—
35#15689657C2212yes—
36#15689657C2212yes—
37#15689657C2212yes—
38#15689657C2212yescomplemented
39#15689657C2212yescomplemented
40C2×#13094018—21no—
41C2×#13094016C2211yescharacteristic
42C2×#13094012C2211yescharacteristic
43#15689634—21no—
44#15689634—21no—
45#15689634C2212yes—
46C2×#13094007—21no—
47C2×#13094003C2211yescharacteristic
48C2×#13093998C2211yescharacteristic
49C4×#10625350—21no—
50C4×#10625350—21no—
51C4×#10625350C2212yes—
52C2×C4×Dic94C2211yescharacteristic
53C2×C4×D188C2211yescharacteristic
54C2×C4×C22⋊D47—21no—
55C2×#13093981—21no—
56#15689431C2214yescomplemented
57#15689431C2214yescomplemented
58#15689431C2214yescomplemented
59#15689424C2214yescomplemented
60#15689424C2214yescomplemented
61#15689424C2214yescomplemented
62#15689419C2212yescomplemented
63#15689414C2212yescomplemented
64#15689409C2212yescomplemented
65#15689404C2212yescomplemented
66#15689381C2214yescomplemented
67#15689376C2214yes—
68#15689369C2214yes—
69#15689369C2214yescomplemented
70#15689364C2214yescomplemented
71#15689359C2214yes—
72#15689352C2214yes—
73#15689352C2214yescomplemented
74#15689346C2214yescomplemented
75#15689346C2214yescomplemented
76#15689346C2214yescomplemented
77#15689339C2214yescomplemented
78#15689339C2214yescomplemented
79#15689339C2214yescomplemented
80#15689334C2212yescomplemented
81#15689329C2212yescomplemented
82#15689324C2212yescomplemented
83#15689319C2212yescomplemented
84#15689165C2212yes—
85#15689165C2212yes—
86#15689133C2212yes—
87#15689129C2212yes—
88#15689125C2212yes—
89#15689125C2212yes—
90C22×M16×C47C2212yes—
91C22×C42×C47C2211yescharacteristic
92C47×#423C2211yescharacteristic
93C47×#423C2211yescharacteristic
94C47×#423C2212yes—
95C47×#423C2212yescomplemented
96C47×#423C2212yescomplemented
97C2×C4⋊C8×C47C2212yescomplemented
98C2×C4⋊C8×C47C2212yescomplemented
99C2×#10625350—21no—
100C2×#10625350—21no—
101C2×#10625350C2312yes—
102C22×Dic94C2311yescharacteristic
103C22×D188C2311yescharacteristic
104C22×C22⋊D47—21no—
105C22×C4×D47—21no—
106#13094057—44no—
107#13094052—44no—
108C2×Dic188C2314yes—
109C2×#10625325C2314yes—
110C2×#10625325C2314yes—
111C2×D376C2314yes—
112#13094024C2311yescharacteristic
113#13094024C2311yescharacteristic
114#13094024C2311yescharacteristic
115#13094021C2311yescharacteristic
116#13094018—22no—
117#13094018—22no—
118#13094018—22no—
119#13094018—22no—
120#13094018—22no—
121#13094018—22no—
122#13094016—21no—
123#13094016—21no—
124#13094016—21no—
125#13094016—21no—
126#13094016C2312yes—
127#13094016C2312yes—
128#13094016C2312yes—
129#13094012—21no—
130#13094012—21no—
131#13094012—21no—
132#13094012—21no—
133#13094012C2312yes—
134#13094012C2312yes—
135#13094012C2312yes—
136#13094007—22no—
137#13094007—22no—
138#13094007—22no—
139#13094007—22no—
140#13094007—22no—
141#13094007—22no—
142#13094007—22no—
143#13094003—21no—
144#13094003—21no—
145#13094003—21no—
146#13094003—21no—
147#13094003—21no—
148#13094003—21no—
149#13094003C2312yes—
150#13094003C2312yes—
151#13094003C2312yes—
152#13094003C2312yes—
153#13093998—21no—
154#13093998—21no—
155#13093998—21no—
156#13093998—21no—
157#13093998—21no—
158#13093998—21no—
159#13093998C2312yes—
160#13093998C2312yes—
161#13093998C2312yes—
162#13093998C2312yes—
163#13093993—22no—
164C4×Dic94—21no—
165C4×Dic94—21no—
166C4×Dic94—21no—
167C4×Dic94—21no—
168C4×Dic94—21no—
169C4×Dic94—21no—
170C4×Dic94C2312yes—
171C4×Dic94C2312yes—
172C4×Dic94C2312yes—
173C4×Dic94C2312yes—
174C4×D188—21no—
175C4×D188—21no—
176C4×D188—21no—
177C4×D188—21no—
178C4×D188—21no—
179C4×D188—21no—
180C4×D188C2312yes—
181C4×D188C2312yes—
182C4×D188C2312yes—
183C4×D188C2312yes—
184C4×C22⋊D47—22no—
185C4×C22⋊D47—22no—
186C4×C22⋊D47—22no—
187C4×C22⋊D47—22no—
188C4×C22⋊D47—22no—
189C4×C22⋊D47—22no—
190C4×C22⋊D47—22no—
191C4×C22⋊D47—22no—
192C4×C22⋊D47—22no—
193C4×C22⋊D47—22no—
194#13093983—21no—
195#13093983—21no—
196#13093983C2312yes—
197#13093981—22no—
198#13093981—22no—
199#13093981—22no—
200#13093981—22no—
201#13093981—22no—
202#13093981—22no—
203#13093981—22no—
204C2×C4⋊Dic47C2311yescharacteristic
205C2×C4⋊Dic47C2311yescharacteristic
206C2×Dic47⋊C4—21no—
207C2×Dic47⋊C4—21no—
208C2×Dic47⋊C4—21no—
209C2×Dic47⋊C4—21no—
210C2×C22⋊Dic47—21no—
211C2×(C2×D47)⋊C4—21no—
212C2×(C2×D47)⋊C4—21no—
213C2×(C2×D47)⋊C4—21no—
214C2×(C2×D47)⋊C4—21no—
215C2×C4×Dic47—21no—
216C42×D47—22no—
217#13093958C2314yes—
218#13093958C2314yes—
219#13093956C2314yes—
220#13093956C2314yes—
221#13093949C2314yes—
222#13093949C2314yes—
223#13093949C2314yes—
224#13093949C2314yes—
225#13093946C2314yes—
226#13093946C2314yes—
227#13093946C2314yes—
228#13093946C2314yes—
229C23×C4×C47D411yescharacteristic
230C23×C4×C47D411yescharacteristic
231C23×C4×C47C2311yescharacteristic
232C2×M16×C47—44no—
233C2×M16×C47C2312yes—
234C2×M16×C47C2312yes—
235C2×M16×C47C2314yes—
236C22×C8×C47C2314yes—
237C2×C42×C47D411yescharacteristic
238C2×C42×C47D411yescharacteristic
239C2×C42×C47D411yescharacteristic
240C2×C42×C47D411yescharacteristic
241C2×C42×C47D411yescharacteristic
242C2×C42×C47D411yescharacteristic
243C2×C42×C47C2311yescharacteristic
244C2×C42×C47C2311yescharacteristic
245C2×C42×C47C2311yescharacteristic
246C2×C42×C47C2311yescharacteristic
247C2×C42×C47C2311yescharacteristic
248C2×C42×C47C2311yescharacteristic
249C4⋊C8×C47C2312yes—
250C4⋊C8×C47C2312yes—
251C4⋊C8×C47C2312yes—
252C4⋊C8×C47C2314yes—
253C4⋊C8×C47C2314yes—
254C4⋊C8×C47C2312yes—
255C24×C47C2×D411yescharacteristic
256C23×D47—21no—
257C22×C4×C47—22no—
258C22×C4×C47—22no—
259C22×C4×C47—42no—
260C22×C4×C47—42no—
261C22×C4×C47C2×D411yescharacteristic
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D411yescharacteristic
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2×D411yescharacteristic
266C22×C4×C47C2×D411yescharacteristic
267C22×C4×C47C2×D411yescharacteristic
268C22×C4×C47C2×D411yescharacteristic
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D411yescharacteristic
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2×D411yescharacteristic
273C22×C4×C47C2×D411yescharacteristic
274C22×C4×C47C2×D411yescharacteristic
275C22×C4×C47C2×D411yescharacteristic
276C22×C4×C47C2411yescharacteristic
277C22×C4×C47C2411yescharacteristic
278C22×C4×C47C2411yescharacteristic
279C2×C22⋊D47—22no—
280C2×C22⋊D47—22no—
281C2×C22⋊D47—22no—
282C2×C22⋊D47—22no—
283C2×C22⋊D47—22no—
284C2×C22⋊D47—44no—
285C22×Dic47—21no—
286C22×Dic47—21no—
287C22×Dic47—21no—
288#10625350—24no—
289#10625350—24no—
290#10625350—44no—
291#10625350—44no—
292C2×D188—22no—
293C2×D188—22no—
294C2×D188—21no—
295C2×D188—21no—
296C2×D188—21no—
297C2×D188C2412yes—
298C2×D188C2412yes—
299C2×C4×D47—22no—
300C2×C4×D47—22no—
301C2×C4×D47—22no—
302C2×C4×D47—22no—
303C2×C4×D47—22no—
304C2×C4×D47—44no—
305C2×Dic94—22no—
306C2×Dic94—22no—
307C2×Dic94—21no—
308C2×Dic94—21no—
309C2×Dic94—21no—
310C2×Dic94C2412yes—
311C2×Dic94C2412yes—
312M16×C47—24no—
313M16×C47—24no—
314M16×C47—44no—
315C2×C8×C47—44no—
316C2×C8×C47C2414yes—
317C2×C8×C47C2414yes—
318C42×C47C2×D411yescharacteristic
319C42×C47C2×D411yescharacteristic
320C42×C47C2×D411yescharacteristic
321C42×C47C2×D411yescharacteristic
322C42×C47C2×D411yescharacteristic
323C42×C47C2×D411yescharacteristic
324C42×C47C2×D411yescharacteristic
325C42×C47C2×D411yescharacteristic
326C42×C47C2×D411yescharacteristic
327C42×C47C2×D411yescharacteristic
328C42×C47C2×D411yescharacteristic
329C42×C47C2×D411yescharacteristic
330C42×C47C2411yescharacteristic
331C42×C47C2411yescharacteristic
332C42×C47C2411yescharacteristic
333C42×C47C2411yescharacteristic
334C22⋊Dic47—22no—
335C22⋊Dic47—22no—
336C22⋊Dic47—22no—
337C22⋊Dic47—22no—
338C22⋊Dic47—22no—
339(C2×D47)⋊C4—22no—
340(C2×D47)⋊C4—22no—
341(C2×D47)⋊C4—22no—
342(C2×D47)⋊C4—22no—
343(C2×D47)⋊C4—22no—
344(C2×D47)⋊C4—22no—
345(C2×D47)⋊C4—22no—
346(C2×D47)⋊C4—22no—
347(C2×D47)⋊C4—22no—
348(C2×D47)⋊C4—22no—
349(C2×D47)⋊C4—22no—
350(C2×D47)⋊C4—22no—
351(C2×D47)⋊C4—22no—
352(C2×D47)⋊C4—22no—
353C4⋊Dic47—21no—
354C4⋊Dic47—21no—
355C4⋊Dic47—21no—
356C4⋊Dic47—21no—
357C4⋊Dic47—21no—
358C4⋊Dic47—21no—
359C4⋊Dic47C2412yes—
360C4⋊Dic47C2412yes—
361C4⋊Dic47C2412yes—
362C4⋊Dic47C2412yes—
363Dic47⋊C4—22no—
364Dic47⋊C4—22no—
365Dic47⋊C4—22no—
366Dic47⋊C4—22no—
367Dic47⋊C4—22no—
368Dic47⋊C4—22no—
369Dic47⋊C4—22no—
370Dic47⋊C4—22no—
371Dic47⋊C4—22no—
372Dic47⋊C4—22no—
373Dic47⋊C4—22no—
374Dic47⋊C4—22no—
375Dic47⋊C4—22no—
376Dic47⋊C4—22no—
377C4×Dic47—22no—
378C4×Dic47—22no—
379C4×Dic47—22no—
380C4×Dic47—22no—
381C4×Dic47—22no—
382Dic188—44no—
383D376—44no—
384#10625325—44no—
385#10625325—44no—
386C23×C47—22no—
387C23×C47—22no—
388C23×C47—41no—
389C23×C47C22×D411yescharacteristic
390C23×C47C22×D411yescharacteristic
391C23×C47C22×D411yescharacteristic
392C22×D47—22no—
393C22×D47—22no—
394C22×D47—42no—
395C22×D47—42no—
396C22×D47—42no—
397C2×C4×C47—22no—
398C2×C4×C47—22no—
399C2×C4×C47—22no—
400C2×C4×C47—22no—
401C2×C4×C47—22no—
402C2×C4×C47—22no—
403C2×C4×C47—22no—
404C2×C4×C47—22no—
405C2×C4×C47—21no—
406C2×C4×C47—21no—
407C2×C4×C47—21no—
408C2×C4×C47—21no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47—41no—
414C2×C4×C47—41no—
415C2×C4×C47—41no—
416C2×C4×C47C22×D411yescharacteristic
417C2×C4×C47C22×D411yescharacteristic
418C2×C4×C47C22×D411yescharacteristic
419C2×C4×C47C22×D411yescharacteristic
420C2×C4×C47C22×D411yescharacteristic
421C2×C4×C47C22×D411yescharacteristic
422C2×C4×C47C22×D411yescharacteristic
423C2×C4×C47C22×D411yescharacteristic
424C2×C4×C47C22×D411yescharacteristic
425C2×C4×C47C22×D411yescharacteristic
426C2×C4×C47C22×D411yescharacteristic
427C2×C4×C47H(5,𝔽2)12yes—
428C2×C4×C472−1+412yes—
429C2×C4×C47C2511yescharacteristic
430C22⋊D47—44no—
431C22⋊D47—44no—
432C22⋊D47—44no—
433C22⋊D47—44no—
434C22⋊D47—44no—
435C2×Dic47—22no—
436C2×Dic47—22no—
437C2×Dic47—22no—
438C2×Dic47—22no—
439C2×Dic47—22no—
440C2×Dic47—22no—
441C2×Dic47—42no—
442C2×Dic47—42no—
443C2×Dic47—42no—
444D188—22no—
445D188—22no—
446D188—22no—
447D188—22no—
448D188—42no—
449D188—42no—
450D188—42no—
451C4×D47—44no—
452C4×D47—44no—
453C4×D47—44no—
454C4×D47—44no—
455C4×D47—44no—
456Dic94—22no—
457Dic94—22no—
458Dic94—22no—
459Dic94—22no—
460Dic94—42no—
461Dic94—42no—
462Dic94—42no—
463C8×C47—24no—
464C8×C47—24no—
465#60917—471nomaximal, Sylow
466C22×C47—21no—
467C22×C47—21no—
468C22×C47—21no—
469C22×C47—21no—
470C22×C47—21no—
471C22×C47—21no—
472C22×C47—21no—
473C22×C47—44no—
474C22×C47#53712yes—
475C22×C47#57512yes—
476C22×C47C23×D411yescharacteristic
477C2×D47—42no—
478C2×D47—42no—
479C2×D47—42no—
480C2×D47—42no—
481C2×D47—42no—
482C2×D47—42no—
483C2×D47—84no—
484C4×C47—21no—
485C4×C47—21no—
486C4×C47—21no—
487C4×C47—21no—
488C4×C47—21no—
489C4×C47—21no—
490C4×C47—21no—
491C4×C47—21no—
492C4×C47—21no—
493C4×C47#53712yes—
494C4×C47#57512yes—
495C4×C47C2×H(5,𝔽2)11yescharacteristic
496C4×C47C2×2−1+411yescharacteristic
497Dic47—42no—
498Dic47—42no—
499Dic47—42no—
500Dic47—42no—
501Dic47—42no—
502Dic47—42no—
503#3444—471no—
504C2×#529—471no—
505#3256—474no—
506#3252—472no—
507#3251—472no—
508#3250—474no—
509#3248—472no—
510#3247—472no—
511#3080—472no—
512#3078—471no—
513#3077—471no—
514#3056—472no—
515#3055—472no—
516#3040—472no—
517#3037—471no—
518#3036—471no—
519C2×#423D4711yescharacteristic, complemented
520C2×C47—22no—
521C2×C47—22no—
522C2×C47—41no—
523C2×C47C2×#53711yescharacteristic
524C2×C47C2×#57511yescharacteristic
525C2×C47C2×#57511yescharacteristic
526D47—82no—
527D47—82no—
528C2×#137—472no—
529C2×AGL(1,ℤ/8)—472no—
530C22×M16C2×D4712yes—
531#533—471no—
532#533—471no—
533#533—471no—
534#532—471no—
535#532—471no—
536#532—471no—
537#529—472no—
538#529—472no—
539#529—472no—
540#529—472no—
541#529—472no—
542#529—472no—
543#529—941no—
544#529—941no—
545#529—941no—
546#529—941no—
547#529—941no—
548#529—941no—
549#529—941no—
550#529—941no—
551C2×#126—941no—
552C2×#125—471no—
553C2×#124—471no—
554#525—472no—
555#525—941no—
556#525—941no—
557C2×#123—941no—
558C2×C22⋊Q8—471no—
559C2×#121—471no—
560C4×#41—472no—
561C4×#41—941no—
562C4×#41—941no—
563C2×C4×Q8—471no—
564C2×C4×D4—471no—
565C2×C4×D4—941no—
566C2×#117—941no—
567C22×C42C2×D4711yescharacteristic
568#479—474no—
569#479—474no—
570#479—474no—
571#478—474no—
572#478—474no—
573#478—474no—
574#477—472no—
575#476—472no—
576#475—472no—
577#474—472no—
578#470—474no—
579#469—474no—
580#468—474no—
581#468—474no—
582#467—474no—
583#466—474no—
584#465—474no—
585#465—474no—
586#464—474no—
587#464—474no—
588#464—474no—
589#463—474no—
590#463—474no—
591#463—474no—
592#462—472no—
593#461—472no—
594#460—472no—
595#459—472no—
596#428—472no—
597#428—472no—
598#423C2×D4711yescharacteristic
599#423C2×D4711yescharacteristic
600#423C2×D4712yes—
601#423C2×D4712yescomplemented
602#423C2×D4712yescomplemented
603C2×C4⋊C8C2×D4712yescomplemented
604C2×C4⋊C8C2×D4712yescomplemented
605#419—472no—
606#418—472no—
607#417—472no—
608#417—472no—
609C47#6091711yescharacteristic, complemented, Sylow
610C2×#41—472no—
611C2×#41—941no—
612C2×#41—941no—
613C22×Q8—471no—
614C22×D4—471no—
615C22×D4—941no—
616C23×C4—941no—
617C23×C4D18811yescharacteristic
618C23×C4D18811yescharacteristic
619C23×C4C22×D4711yescharacteristic
620#137—1884no—
621AGL(1,ℤ/8)—1884no—
622C2×Q16—474no—
623C2×SD16—474no—
624C2×SD16—474no—
625C2×D8—474no—
626C2×M16—44no—
627C2×M16C22×D4712yes—
628C2×M16C22×D4712yes—
629C2×M16C22×D4714yes—
630C22×C8C22×D4714yes—
631C4⋊Q8—471no—
632C4⋊Q8—471no—
633C4⋊Q8—471no—
634#127—471no—
635#126—942no—
636#126—942no—
637#126—942no—
638#126—942no—
639#126—942no—
640#126—942no—
641#125—472no—
642#125—472no—
643#125—472no—
644#125—941no—
645#125—941no—
646#125—941no—
647#125—941no—
648#124—472no—
649#124—472no—
650#124—472no—
651#124—941no—
652#124—941no—
653#124—941no—
654#124—941no—
655#123—942no—
656#123—942no—
657#123—942no—
658#123—942no—
659#123—942no—
660#123—942no—
661#123—942no—
662C22⋊Q8—472no—
663C22⋊Q8—472no—
664C22⋊Q8—472no—
665C22⋊Q8—472no—
666C22⋊Q8—941no—
667C22⋊Q8—941no—
668C22⋊Q8—941no—
669C22⋊Q8—941no—
670C22⋊Q8—941no—
671C22⋊Q8—941no—
672#121—472no—
673#121—472no—
674#121—472no—
675#121—472no—
676#121—941no—
677#121—941no—
678#121—941no—
679#121—941no—
680#121—941no—
681#121—941no—
682#120—942no—
683C4×Q8—472no—
684C4×Q8—472no—
685C4×Q8—472no—
686C4×Q8—472no—
687C4×Q8—941no—
688C4×Q8—941no—
689C4×Q8—941no—
690C4×Q8—941no—
691C4×Q8—941no—
692C4×Q8—941no—
693C4×D4—472no—
694C4×D4—472no—
695C4×D4—472no—
696C4×D4—472no—
697C4×D4—942no—
698C4×D4—942no—
699C4×D4—942no—
700C4×D4—942no—
701C4×D4—942no—
702C4×D4—942no—
703C4×D4—942no—
704C4×D4—942no—
705C4×D4—942no—
706C4×D4—942no—
707C4×D4—941no—
708C4×D4—941no—
709C4×D4—941no—
710C4×D4—941no—
711C4×D4—941no—
712C4×D4—941no—
713#117—472no—
714#117—941no—
715#117—941no—
716#117—942no—
717#117—942no—
718#117—942no—
719#117—942no—
720#117—942no—
721#117—942no—
722#117—942no—
723C2×C4⋊C4—471no—
724C2×C4⋊C4—471no—
725C2×C4⋊C4—941no—
726C2×C4⋊C4—941no—
727C2×C4⋊C4—941no—
728C2×C4⋊C4—941no—
729C2×C22⋊C4—941no—
730C2×C22⋊C4—941no—
731C2×C22⋊C4—941no—
732C2×C22⋊C4—941no—
733C2×C22⋊C4—941no—
734C2×C42—941no—
735C2×C42—942no—
736C2×C42D18811yescharacteristic
737C2×C42D18811yescharacteristic
738C2×C42D18811yescharacteristic
739C2×C42D18811yescharacteristic
740C2×C42D18811yescharacteristic
741C2×C42D18811yescharacteristic
742C2×C42C22×D4711yescharacteristic
743C2×C42C22×D4711yescharacteristic
744C2×C42C22×D4711yescharacteristic
745C2×C42C22×D4711yescharacteristic
746C2×C42C22×D4711yescharacteristic
747C2×C42C22×D4711yescharacteristic
748#107—474no—
749#107—474no—
750#106—474no—
751#106—474no—
752C4⋊C8C22×D4712yes—
753C4⋊C8C22×D4712yes—
754C4⋊C8C22×D4712yes—
755C4⋊C8C22×D4714yes—
756C4⋊C8C22×D4714yes—
757C4⋊C8C22×D4712yes—
758#103—474no—
759#103—474no—
760#103—474no—
761#103—474no—
762#102—474no—
763#102—474no—
764#102—474no—
765#102—474no—
766C24—941no—
767C24C2×D18811yescharacteristic
768#41—944no—
769#41—944no—
770#41—1884no—
771#41—1884no—
772C2×Q8—472no—
773C2×Q8—472no—
774C2×Q8—941no—
775C2×Q8—941no—
776C2×Q8—941no—
777C2×Q8—942no—
778C2×Q8—942no—
779C2×D4—472no—
780C2×D4—472no—
781C2×D4—942no—
782C2×D4—942no—
783C2×D4—942no—
784C2×D4—942no—
785C2×D4—942no—
786C2×D4—941no—
787C2×D4—941no—
788C2×D4—941no—
789C2×D4—942no—
790C2×D4—942no—
791C2×D4—1884no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—941no—
797C22×C4—941no—
798C22×C4—941no—
799C22×C4—942no—
800C22×C4—942no—
801C22×C4—942no—
802C22×C4—942no—
803C22×C4—942no—
804C22×C4—1884no—
805C22×C4C2×D18811yescharacteristic
806C22×C4C2×D18811yescharacteristic
807C22×C4C2×D18811yescharacteristic
808C22×C4C2×D18811yescharacteristic
809C22×C4C2×D18811yescharacteristic
810C22×C4C2×D18811yescharacteristic
811C22×C4C2×D18811yescharacteristic
812C22×C4C2×D18811yescharacteristic
813C22×C4C2×D18811yescharacteristic
814C22×C4C2×D18811yescharacteristic
815C22×C4C2×D18811yescharacteristic
816C22×C4C2×D18811yescharacteristic
817C22×C4C2×D18811yescharacteristic
818C22×C4C2×D18811yescharacteristic
819C22×C4C2×D18811yescharacteristic
820C22×C4C23×D4711yescharacteristic
821C22×C4C23×D4711yescharacteristic
822C22×C4C23×D4711yescharacteristic
823Q16—1884no—
824SD16—1884no—
825SD16—1884no—
826D8—1884no—
827M16—24no—
828M16—24no—
829M16—44no—
830C2×C8—44no—
831C2×C8C23×D4714yes—
832C2×C8C23×D4714yes—
833C4⋊C4—472no—
834C4⋊C4—472no—
835C4⋊C4—472no—
836C4⋊C4—472no—
837C4⋊C4—942no—
838C4⋊C4—942no—
839C4⋊C4—942no—
840C4⋊C4—942no—
841C4⋊C4—942no—
842C4⋊C4—942no—
843C4⋊C4—942no—
844C4⋊C4—942no—
845C4⋊C4—942no—
846C4⋊C4—942no—
847C4⋊C4—942no—
848C4⋊C4—942no—
849C4⋊C4—942no—
850C4⋊C4—942no—
851C4⋊C4—941no—
852C4⋊C4—941no—
853C4⋊C4—941no—
854C4⋊C4—941no—
855C4⋊C4—941no—
856C4⋊C4—941no—
857C22⋊C4—942no—
858C22⋊C4—942no—
859C22⋊C4—942no—
860C22⋊C4—942no—
861C22⋊C4—942no—
862C22⋊C4—942no—
863C22⋊C4—942no—
864C22⋊C4—942no—
865C22⋊C4—942no—
866C22⋊C4—942no—
867C22⋊C4—942no—
868C22⋊C4—942no—
869C22⋊C4—942no—
870C22⋊C4—942no—
871C22⋊C4—942no—
872C22⋊C4—942no—
873C22⋊C4—942no—
874C22⋊C4—942no—
875C22⋊C4—942no—
876C42—942no—
877C42—942no—
878C42—942no—
879C42—942no—
880C42—942no—
881C42C2×D18811yescharacteristic
882C42C2×D18811yescharacteristic
883C42C2×D18811yescharacteristic
884C42C2×D18811yescharacteristic
885C42C2×D18811yescharacteristic
886C42C2×D18811yescharacteristic
887C42C2×D18811yescharacteristic
888C42C2×D18811yescharacteristic
889C42C2×D18811yescharacteristic
890C42C2×D18811yescharacteristic
891C42C2×D18811yescharacteristic
892C42C2×D18811yescharacteristic
893C42C23×D4711yescharacteristic
894C42C23×D4711yescharacteristic
895C42C23×D4711yescharacteristic
896C42C23×D4711yescharacteristic
897C23—22no—
898C23—22no—
899C23—41no—
900C23—942no—
901C23—942no—
902C23—1882no—
903C23—1882no—
904C23—1882no—
905C23C22×D18811yescharacteristic
906C23C22×D18811yescharacteristic
907C23C22×D18811yescharacteristic
908Q8—942no—
909Q8—942no—
910Q8—942no—
911Q8—942no—
912Q8—1882no—
913Q8—1882no—
914Q8—1882no—
915D4—942no—
916D4—942no—
917D4—942no—
918D4—942no—
919D4—1882no—
920D4—1884no—
921D4—1884no—
922D4—1884no—
923D4—1884no—
924D4—1884no—
925D4—1882no—
926D4—1882no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—942no—
947C2×C4—942no—
948C2×C4—942no—
949C2×C4—942no—
950C2×C4—942no—
951C2×C4—942no—
952C2×C4—1884no—
953C2×C4—1884no—
954C2×C4—1884no—
955C2×C4—1882no—
956C2×C4—1882no—
957C2×C4—1882no—
958C2×C4—1884no—
959C2×C4—1884no—
960C2×C4C22×D18811yescharacteristic
961C2×C4C22×D18811yescharacteristic
962C2×C4C22×D18811yescharacteristic
963C2×C4C22×D18811yescharacteristic
964C2×C4C22×D18811yescharacteristic
965C2×C4C22×D18811yescharacteristic
966C2×C4C22×D18811yescharacteristic
967C2×C4C22×D18811yescharacteristic
968C2×C4C22×D18811yescharacteristic
969C2×C4C22×D18811yescharacteristic
970C2×C4C22×D18811yescharacteristic
971C2×C4#1309406912yes—
972C2×C4#1309407212yes—
973C2×C4C24×D4711yescharacteristic
974C8—24no—
975C8—24no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—44no—
984C22—3764no—
985C22—1882no—
986C22—1882no—
987C22—1882no—
988C22—1882no—
989C22—1882no—
990C22—1882no—
991C22#1568970412yes—
992C22#1568992312yes—
993C22C23×D18811yescharacteristic
994C4—21no—
995C4—21no—
996C4—21no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—21no—
1001C4—21no—
1002C4—21no—
1003C4—1882no—
1004C4—1882no—
1005C4—1882no—
1006C4—1882no—
1007C4—1882no—
1008C4—1882no—
1009C4#1568970412yes—
1010C4#1568992312yes—
1011C4C2×#1309406911yescharacteristic
1012C4C2×#1309407211yescharacteristic
1013C2—22no—
1014C2—22no—
1015C2—41no—
1016C2—3762no—
1017C2—3762no—
1018C2C2×#1568970411yescharacteristic
1019C2C2×#1568992311yescharacteristic
1020C2C2×#1568992311yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#423C2
socleC22×C47C23×D4
hypercenterC2×#423D47
hypocenterC47#60917
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#423

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20256684C2semidirect
2. C2×#15689657C2semidirect
3. #20254789C2semidirect
4. #20254762C2semidirect
5. #20254751C2semidirect
6. #20254740C2semidirect
7. #20254726C2semidirect
8. #20254715C2semidirect
9. #20253211C2semidirect
10. #20253195C2semidirect
11. #20253187C2semidirect
12. #20253018C2semidirect
13. #20253007C2semidirect
14. #20252883C2semidirect
15. #20252862C2semidirect
16. #20252854C2semidirect
17. C2×C47×#423C2semidirect
21. #15689680C22semidirect
22. #15689680C22semidirect
24. #15689673C22semidirect
25. #15689673C22semidirect
38. #15689657C22semidirect
39. #15689657C22semidirect
56. #15689431C22semidirect
57. #15689431C22semidirect
58. #15689431C22semidirect
59. #15689424C22semidirect
60. #15689424C22semidirect
61. #15689424C22semidirect
62. #15689419C22semidirect
63. #15689414C22semidirect
64. #15689409C22semidirect
65. #15689404C22semidirect
66. #15689381C22semidirect
69. #15689369C22semidirect
70. #15689364C22semidirect
73. #15689352C22semidirect
74. #15689346C22semidirect
75. #15689346C22semidirect
76. #15689346C22semidirect
77. #15689339C22semidirect
78. #15689339C22semidirect
79. #15689339C22semidirect
80. #15689334C22semidirect
81. #15689329C22semidirect
82. #15689324C22semidirect
83. #15689319C22semidirect
95. C47×#423C22semidirect
96. C47×#423C22semidirect
97. C2×C4⋊C8×C47C22semidirect
98. C2×C4⋊C8×C47C22semidirect
519. C2×#423D47semidirect
601. #423C2×D47semidirect
602. #423C2×D47semidirect
603. C2×C4⋊C8C2×D47semidirect
604. C2×C4⋊C8C2×D47semidirect
609. C47#60917semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202566842
C2×#156896572
#202547892
#202547622
#202547512
#202547402
#202547262
#202547152
#202532112
#202531952
#202531872
#202530182
#202530072
#202528832
#202528622
#202528542
C2×C47×#4232
#6091747